Guided wave opto-acoustic device

ABSTRACT

The various technologies presented herein relate to various hybrid phononic-photonic waveguide structures that can exhibit nonlinear behavior associated with traveling-wave forward stimulated Brillouin scattering (forward-SBS). The various structures can simultaneously guide photons and phonons in a suspended membrane. By utilizing a suspended membrane, a substrate pathway can be eliminated for loss of phonons that suppresses SBS in conventional silicon-on-insulator (SOI) waveguides. Consequently, forward-SBS nonlinear susceptibilities are achievable at about 3000 times greater than achievable with a conventional waveguide system. Owing to the strong phonon-photon coupling achievable with the various embodiments, potential application for the various embodiments presented herein cover a range of radiofrequency (RF) and photonic signal processing applications. Further, the various embodiments presented herein are applicable to applications operating over a wide bandwidth, e.g. 100 MHz to 50 GHz or more.

RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationNo. 61/785,163 filed on Mar. 14, 2013, entitled “GUIDED WAVEOPTO-ACOUSTIC DEVICE AND METHODS FOR MAKING THE SAME”, the entirety ofwhich is incorporated herein by reference.

STATEMENT OF GOVERNMENTAL INTEREST

This invention was developed under contract DE-AC04-94AL85000 betweenSandia Corporation and the U.S. Department of Energy. The U.S.Government has certain rights in this invention.

BACKGROUND

Photon-phonon coupling through guided-wave stimulated Brillouinscattering (SBS) is finding application in numerous technology fieldssuch as tailorable slow light, radio frequency (RF)-photonic signalprocessing, narrow-line-width laser sources, RF-waveform synthesis,optical frequency comb generation, etc. Realization of this form oftravelling-wave photon-phonon coupling in a silicon-based and CMOS(complementary metal-oxide-semiconductor)-compatible platform can enablehigh-performance signal-processing applications through nanoscaleBrillouin interactions. Nanoscale modal confinement can enhancenon-linear lightmatter interactions within silicon waveguides and innanooptomechanics. For instance, tight optical confinement in nanoscalesilicon waveguides can be responsible for greatly enhanced Raman andKerr non-linearities, and for new sensing, actuation and transductionmechanisms based on optical forces within nano-optomechanical systems.

The field of cavity optomechanics has produced a wide variety of systemswith enhanced and controllable forms of photon-phonon coupling.Specifically, silicon (Si)-based cavityoptomechanical systems haveenabled powerful new forms of quantum state transfer, slow light, phononlasers and optomechanical ground-state cooling. Such cavity systemsexploit resonantly enhanced coupling between discrete photonic andphononic modes. As a fundamental complement to cavity systems,guided-wave Brillouin processes can produce coupling between a continuumof photon and phonon modes for a host of wideband (e.g., 0.1-34 GHz) RFand photonic signal-processing applications. For example,travelling-wave Brillouin processes have enabled unique schemes foroptical pulse compression, pulse and waveform synthesis, coherentfrequency comb generation, variable bandwidth optical amplifiers,reconfigurable filters and coherent beam-combining schemes. Althoughthere are numerous applications and opportunities for chip-scaleBrillouin technologies, the ability for conventional systems to achieveBrillouin processes in silicon nanophotonics has proven difficult;strong Brillouin nonlinearities require large optical forces and tightconfinement of both phonons and photons, conditions that are not met inconventional Si waveguides.

SUMMARY

The following is a brief summary of subject matter that is described ingreater detail herein. This summary is not intended to be limiting as tothe scope of the claims.

Various exemplary embodiments presented herein relate to photon-phononcoupling through a guided-wave stimulated Brillouin scattering. In anexemplary embodiment an apparatus is presented, the apparatus comprisinga suspended membrane, whereby at least one optical waveguiding member isincluded in the membrane and at least partially extensive in alongitudinal optical propagation direction. The apparatus furthercomprising at least one phononic resonator defined in the membrane,extensive in said longitudinal direction, and traversed by the opticalwaveguiding member.

Another exemplary embodiment is presented comprising a method forforming photon-phonon coupling waveguide device, the method comprisingdepositing an insulating layer on a substrate whereupon a waveguidingmember is subsequently formed on the insulating layer. A membrane layercan be deposited on the insulating layer and on the waveguiding membersuch that the deposited membrane layer abuts and overlies thewaveguiding member. The method further comprising removing such of themembrane layer as overlies the waveguiding member. The membrane layercan be patterned so as to define therein at least one longitudinallyextensive phononic resonator traversed by the waveguiding member. Themethod further comprising removing at least a portion of the insulatinglayer that underlies the membrane layer, including such portion asunderlies the longitudinally extensive phononic resonator or resonators.

A further exemplary embodiment for photon-phonon coupling in a waveguidedevice can comprise a method which can include injecting a first opticalpulse and a second optical pulse into a waveguide core, wherein thewaveguide core is supported on a membrane, the first pulse and thesecond pulse combining to facilitate creation of one or more phonons,the phonon propagating through the membrane in a direction transverse toan optical direction of the waveguide core and the propagating of thephonon causing amplification of the second pulse.

The above summary presents a simplified summary in order to provide abasic understanding of some aspects of the systems and/or methodsdiscussed herein. This summary is not an extensive overview of thesystems and/or methods discussed herein. It is not intended to identifykey/critical elements or to delineate the scope of such systems and/ormethods. Its sole purpose is to present some concepts in a simplifiedform as a prelude to the more detailed description that is presentedlater.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a waveguide device, according to anembodiment.

FIG. 2 is a scanning electron micrograph of a waveguide core andmembrane, according to an embodiment.

FIG. 3 is a scanning electron micrograph of a waveguide devicecomprising a plurality of waveguide regions, according to an embodiment.

FIG. 4 is a schematic of phonons being formed tranverse to a directionof an optical wave, according to an embodiment.

FIG. 5 illustrates propagation of a guided elastic phonon mode at awaveguide and across respective membrane regions, according to anembodiment.

FIG. 6 illustrates propagation of an optical mode at a waveguide andacross respective membrane regions, according to an embodiment.

FIG. 7 presents vector phase matching diagrams for respective Stokes andanti-Stokes forward-stimulated Brillouin scattering, according to anembodiment.

FIG. 8 is a schematic of phonons being formed tranverse to a directionof an optical wave, according to an embodiment.

FIG. 9 presents a cross-section through a waveguide and membraneregions, according to an embodiment.

FIG. 10 depicts a computed E_(x) optical field distribution of theoptical mode, according to an embodiment.

FIG. 11 depicts a x-component of an electrostrictive (ES) force densitygenerated within a waveguide, according to an embodiment.

FIG. 12 depicts a y-component of an electrostrictive (ES) force densitygenerated within a waveguide, according to an embodiment.

FIG. 13 presents a schematic of an electrostrictive induced boundaryforce produced by an optical mode, according to an embodiment.

FIG. 14 presents a schematic of a radiation pressure (RP)-inducedboundary force produced by an optical mode, according to an embodiment.

FIG. 15 presents a chart of dispersion curves illustrating phononfrequency versus longitudinal wave vector of various Brillouin-activephonon modes, according to an embodiment.

FIG. 16 presents a representation of an optical wave vector mismatch,Δk, produced by the dispersion of the optical waveguide mode, ω(k), aspump and Stokes waves are detuned, according to an embodiment.

FIG. 17 depicts a displacement field associated with a phasematchedBrillouin-active guided wave for a first mode, according to anembodiment.

FIG. 18 depicts a displacement field associated with a phasematchedBrillouin-active guided wave for a second mode, according to anembodiment.

FIG. 19 depicts a displacement field associated with a phasematchedBrillouin-active guided wave for a third mode, according to anembodiment.

FIG. 20 depicts a displacement field associated with a phasematchedBrillouin-active guided wave for a fourth mode, according to anembodiment.

FIG. 21 depicts a displacement field associated with a phasematchedBrillouin-active guided wave for a fifth mode, according to anembodiment.

FIG. 22 depicts a displacement field associated with a phasematchedBrillouin-active guided wave for a sixth mode, according to anembodiment.

FIG. 23 depicts a displacement field associated with a phasematchedBrillouin-active guided wave for a seventh mode, according to anembodiment.

FIG. 24 presents signatures of non-linear Brillouin response as afunction of pump signal modulation, according to an embodiment.

FIG. 25 is a high-resolution spectral scans of a line shape of acharacteristic Brillouin resonance decomposed to its Stokes component,according to an embodiment.

FIG. 26 is a high-resolution spectral scans of a line shape of acharacteristic Brillouin resonance decomposed to its anti-Stokescomponent, according to an embodiment.

FIG. 27 presents a plurality of resonances spanning a range offrequencies, according to an embodiment.

FIG. 28 presents contributions of ES forces, radiation pressure andthermoelastic expansion to a total SBS nonlinear coefficient for aplurality of phonon resonance modes, according to an embodiment.

FIG. 29 presents peak values for measured and simulated Brillouincoupling for a plurality of resonances, according to an embodiment.

FIG. 30 presents peak values for a phononic Q-factor for a plurality ofresonances, according to an embodiment.

FIG. 31 presents Stokes and anti-Stokes components as a function of RFfrequency versus power, according to an embodiment.

FIG. 32 presents normalized Stokes transmittances for a variety of pumppowers, according to an embodiment.

FIG. 33 presents normalized anti-Stokes transmittances for a variety ofpump powers, according to an embodiment.

FIG. 34 presents a relationship between pump power and amplification forStokes and anti-Stokes transmittances.

FIG. 35 is a schematic diagram of a waveguide device, according to anembodiment.

FIG. 36 is a schematic diagram of a waveguide device comprising twowaveguides, according to an embodiment.

FIG. 37 is a schematic diagram of a confocal waveguide device, accordingto an embodiment.

FIG. 38 illustrates a waveguide device being utilized in conjunctionwith a circular resonant waveguide, according to an embodiment.

FIGS. 39-44 illustrate various stages in fabrication of a waveguidedevice, according to at least one embodiment.

FIG. 45 is a scanning electron micrograph of a dual photonic crystalwaveguide, according to an embodiment.

FIG. 46 is a schematic of a dual photonic crystal waveguide operatingbelow a bandgap frequency, according to an embodiment.

FIG. 47 is a schematic of a dual photonic crystal waveguide operating ata bandgap frequency, according to an embodiment.

FIG. 48 is a chart illustrating conversion efficiency versus frequencyfor a dual photonic crystal waveguide, according to an embodiment.

FIG. 49 is a flow diagram illustrating an exemplary methodology foroperating a waveguide device to amplify light, according to anembodiment.

DETAILED DESCRIPTION

Various technologies are presented herein relating to photon-phononcoupling through a guided-wave stimulated Brillouin scattering (SBS),wherein like reference numerals are used to refer to like elementsthroughout. In the following description, for purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of one or more aspects. It may be evident, however, thatsuch aspect(s) may be practiced without these specific details. In otherinstances, well-known structures and devices are shown in block diagramform in order to facilitate describing one or more aspects.

Further, the term “or” is intended to mean an inclusive “or” rather thanan exclusive “or”. That is, unless specified otherwise, or clear fromthe context, the phrase “X employs A or B” is intended to mean any ofthe natural inclusive permutations. That is, the phrase “X employs A orB” is satisfied by any of the following instances: X employs A; Xemploys B; or X employs both A and B. In addition, the articles “a” and“an” as used in this application and the appended claims shouldgenerally be construed to mean “one or more” unless specified otherwiseor clear from the context to be directed to a singular form.Additionally, as used herein, the term “exemplary” is intended to meanserving as an illustration or example of something, and is not intendedto indicate a preference.

The various embodiments presented herein relate to various hybridphononic-photonic waveguide structures that can exhibit nonlinearbehavior associated with traveling-wave forward stimulated Brillouinscattering (forward-SBS). The various structures can simultaneouslyguide photons and phonons in a suspended membrane. By utilizing asuspended membrane, it is possible to eliminate a substrate pathway forloss of phonons that suppresses SBS in conventional silicon-on-insulator(SOI) waveguides. Consequently, forward-SBS nonlinear susceptibilitiesare achievable with a Brillouin non-linear coefficient that is more thanabout 3000 times greater than achievable with a conventional waveguidesystem. Owing to the strong phonon-photon coupling achievable with thevarious embodiments herein, potential application for the variousembodiments presented herein cover a range of radiofrequency (RF) andphotonic signal processing applications, including pulse compression,pulse and waveform synthesis, coherent frequency comb generation,optical amplification, optical filtration, coherent beam combining, etc.Further, the various embodiments presented herein are applicable toapplications operating over a wide bandwidth, e.g. 100 MHz to 50 GHz ormore.

Further presented herein is experimental data related to measuring theBrillouin nonlinearity of a waveguide, whereby pump radiation at 1556 nmwas intensity modulated at a variable RF frequency Ω/2 to produce twosidebands respectively upshifted and downshifted by the RF frequency.The modulated pump radiation was mixed with probe radiation at 1536 nmand injected into the waveguide. Interference between the sidebands atthe beat frequency Ω produced Stokes and anti-Stokes shifted proberadiation by forward-SBS at values of Ω that correspond to phononicresonances. The waveguide output was filtered to remove the pumpradiation, and the frequency-shifted probe radiation was measured in aheterodyne detector that combined the filtered waveguide output with alocal oscillator signal produced by imposing a small frequency offset ona tapped-off portion of the 1536-nm probe radiation.

FIGS. 1-4 illustrate various views and sections of a waveguide device100 configured to facilitate photon-phonon coupling through aguided-wave stimulated Brillouin scattering (SBS), according to anembodiment. Waveguide device 100 can comprise a Brillouin-activemembrane waveguide (also referred to as a BAM waveguide). FIG. 1 is anend-on, 3-dimensional representation of the waveguide device 100, takenfrom region A of FIG. 3. FIG. 2 is a scanning electron micrograph of awaveguide core region comprising a waveguide core 130 and adjacentmembrane 140. FIG. 3 is scanning electron micrograph of a top down viewin direction X, depicting a portion of a waveguide device 100comprising, in series, three identical membrane-suspended regions.Region A indicates the location of FIG. 1 relative to FIG. 3, and regionB indicates the location of FIG. 4 relative to FIG. 3. FIG. 4illustrates an optical wave being transmitted into a waveguide device100 and the resulting phonon distribution occurring in phonic regions170 and 180. A shown in FIGS. 1-4, device 100 can comprise a substrate110, having formed thereon an insulator layer 120. Located over a cavity160 formed in the insulator layer 120, is a membrane 140, whereinmembrane layer 140 has a plurality of slots 150 and 155, with membraneregions 170 and 180 juxtaposing a waveguide core 130.

Any suitable material can be utilized for the respective structuralelements comprising waveguide device 100. For example, substrate 110 canbe formed from silicon (Si), insulator layer 120 can be formed fromsilicon dioxide, SiO₂, waveguide 130 can be formed from any suitablewaveguide forming material, such as Si, and membrane 140 can be formedfrom silicon nitride (Si₃N₄), whereby the membrane layer 140 can be in astate of tension. In an embodiment, waveguide 130 can be nanophotonic,and further can have dimensions width w=313 nm and height h=194 nm,while membrane 140 can have a thickness t=124 nm.

As described further herein, slots 150 and 155 can be utilized tofacilitate formation of a cavity 160. Slots 150 and 155 can be furtherutilized to effectively operate as a reflector of acoustic waves havingwavevectors substantially transverse (e.g., direction P) to an opticalpropagation direction (e.g., direction O). Hence each pair of slots(e.g., slots 150 and 155) can form an acoustic resonator capable ofdefining a series of discrete phononic resonances in at least the rangeof 1-18 GHz. In the exemplary embodiment, slots 150 and 155 can be 2 μmwide by 100 μm long. Hence, regions 170 and 180 are accordinglytruncated on either side of the waveguide 130 by the symmetricallyplaced slots 150 and 155. The geometry of device 100 can facilitateindependent control of the photonic and phononic properties of aBrillouin waveguide, enabling the phonon mode spectrum to be tailoredindependently from the optical force distributions within the core ofthe waveguide 130.

FIGS. 5 and 6 illustrate respective propagation of the guided elasticand optical modes at a waveguide 130 and across respective membraneregions 170 and 180. Further, FIG. 7 presents vector phase matchingdiagrams 710 and 720 for respective Stokes and anti-Stokesforward-stimulated Brillouin scattering, whereby k_(p) represents theoptical pump, k_(s) represents the Stokes wave-vector, k_(a) representsthe anti-Stokes wave-vector and K is the phonon wave-vector. As shown inFIGS. 5 and 6, phase matching can necessitate a vanishing longitudinalphonon wave-vector through forward-SBS, resulting in standing phononmodes (or slow group velocity resonant guided phononic modes) with largetransverse wave-vectors. As further shown in FIGS. 5 and 6, owing to thetotal internal reflection between Si (n=3.5) comprising the waveguide130, and Si₃N₄ (n=2.0), forming the membrane 140, the respective Si andSi₃N₄ regions can act to tightly confine the optical mode of waveguidedevice 100 to the waveguide core 130. Further, the patterned membrane140 (e.g., comprising regions 170 and 180 with respective slots 150 and155) can act to guide and/or confine the generated phonons. Thecompound-material geometry of waveguide device 100 can provideindependent control of the photonic and phononic waveguide dispersion,which can facilitate the phonon modes to be shaped separately from theoptical forces within the core of the waveguide 130

FIG. 8 illustrates a schematic 800 of a displacement field of a phononexcited by optical forces within a waveguide device 100 (also referredto as a transversely oriented phonon-resonator optical waveguide(TOPROW)) as a function of intramodal forward SBS through Brillouincoupling between guided transverse-electric-like optical modes. FIG. 8presents a displacement field of a 3.7 GHZ extended phonon excited byoptical forces within waveguide 130 operating in conjunction with amembrane 140. In an embodiment, d=3.8 μm and L=100 μm. A modulator 810can be configured to modulate pump light 812 received from a pump sourcein response to a radiofrequency waveform 815 received from aradiofrequency generator. An input combiner 830 can be configured tocombine an optical input signal 840 with the modulated pump light 820and to inject the combined light 850 into an optical waveguiding device100. Waveguiding device 100 can comprise a waveguide core 130, slots 150and 155, and phononic regions 170 and 180, as previously described. Anoutput coupling element 870 can be configured to extract an outputoptical signal 880 from an optical waveguiding device 100.

FIG. 9 presents a cross-section through a waveguide 130 and membraneregions 170 and 180 to facilitate understanding of the followingrepresentations. FIG. 10 depicts a computed E_(x) optical fielddistribution of the optical mode. Computed electrostriction (ES) forcedensities are shown in FIGS. 11-13, where FIGS. 11 and 12 presentrespective x- and y-components of the electrostrictive (ES) forcedensities generated within the waveguide 130. The force densities arepresented for an embodiment where the waveguide 130 comprises Si. FIG.13 presents electrostrictive induced boundary forces produced by theoptical mode. FIG. 14 illustrates a radiation pressure (RP)-inducedforce density. The respective force densities presented in FIGS. 11-14can facilitate mediation of Brillouin coupling. Through forward SBS,co-propagating pump and Stokes waves of frequencies ω_(p) and ω_(s),couple through parametrically generated acoustic phonons of differencefrequency Ω=ω_(p)−ω_(s). Momentum conservation requires thatk(ω_(p))=K(Ω)=k(ω_(s)), where k(ω) is the optical dispersion relation,and K(Ω) is the phonon-dispersion relation. Thus, strong photon-phononcoupling is mediated by the set of phonons, {Ω_(i)}, whose dispersionrelations satisfy the phasematching conditionΔk(Ω)=k(ω_(p))−k(ω_(p)−Ω)=K(Ω).

FIG. 15 presents a chart 1500 of dispersion curves illustrating phononfrequency versus longitudinal wave vector of various Brillouin-activephonon modes, e.g., for a waveguide device 100 having a dimension d=3.8μm. In an aspect, only the phonon modes (e.g., m=1, m=2, . . . m=7) thatexhibit strong Brillouin coupling through good overlap between anelastic displacement field and an optical force distribution are shown.Plot 1510 presents the optical wave vector mismatch, Δk(Ω), which isplotted atop the various plots 1520 of phononic dispersion relation,K(Ω). For small wave vectors (e.g., on the left of FIG. 15), thephase-matched phonons, as presented as circles on FIG. 15, areidentified by the intersection between the optical wave vector mismatch(e.g., diagonal plot 1510) and the Brillouin-active phonon modes (e.g.,respective horizontal lines 1520 marked m=1, m=2, . . . m=7). The pointsof intersection between plots 1510 and respective plots 1520 for eachm=1-7 identify the Ω- and K-values of the phase-matched phonon modes.Numerous phase-matched phonon modes m=1-7 are presented with evenlyspaced frequencies spanning 1-16 GHz, and corresponding values of |K| ofbetween 1.3 and 17 rad cm⁻¹. In an aspect, the waveguide device 100 cancomprise a number of periodic-array Brillouin-active suspended regions,as seen by the SEM micrograph of FIG. 3. If the spatial period of awaveguide is smaller than the longitudinal period of the guided phononwave vector (2π/|K|), the phase-matching conditions will be unaffected.Here, that is true as the spatial period of the waveguide modulation(e.g., 125 μm) is more than 20 times smaller than the longitudinalperiod of the guided phonon wave vector.

On the basis of the phase-matching condition and the relation|ΔK(Ω)|≅(∂|k|/∂ω)Ω=(Ω/ν_(g)), only guided phonons with phase velocitiesmatching the group velocity of light (ν_(g)) produce resonant couplingthrough forward SBS. Such an effect can be a result of the interferencebetween the co-propagating pump and Stokes waves. In an embodiment, theinterference yields modulated energy density and force densitydistributions that propagate along the waveguide at the group velocity(ν_(g)) of light. As this travelling-force distribution drivesphoton-phonon coupling, only phonons with phase velocities (Ω/K)matching the group velocity (ν_(g)) of light can produce efficientcoupling (e.g., as presented as circles in FIG. 15). These ultra-highphase-velocity-guided phonon modes (e.g., of about 10⁸ ms⁻¹) havecorresponding guided phonon group velocities (∂Ω/∂K) that areexceedingly slow (˜1 ms⁻¹), but are non-zero.

The displacement field associated with each of the phase-matchedBrillouin-active guided wave modes, m=1-7, are shown in FIGS. 17-23.Labeling of each mode (e.g., m=1, m=2, . . . m=7) is according to themode index identified in FIG. 15. Further, the right half membraneregion 180 of each displacement field is shown in each of FIGS. 17-23.The symmetric force distributions, as presented in FIGS. 11-14, permitcoupling of photons in the waveguide core 130 to phonons with symmetricdisplacement fields about the waveguide core 130. Hence, it can beconsidered that the membrane regions 170 will undergo the same effectsas the illustrated modes of FIGS. 17-23. Periodic boundary conditionscan be applied to the z-normal faces of the simulations to facilitatecomputation of the displacement fields of the phase-matched phonon modespresented in FIGS. 17-23 and the corresponding phonon-dispersion curvesin FIG. 15. Although these guided elastic modes can exhibit someflexural character, the vast majority of the modal potential energy canbe ascribed to in-plane elastic compression (e.g., FIG. 8, directionsx-z). The compressive character of these slow group velocity-guidedmodes can be most clearly seen in the high frequency limit, asdemonstrated by the displacement fields of FIG. 22, m=6, and FIG. 23,m=7. For small K-values, the z-component of the phonon displacementfield can become much smaller than the x-component. Moreover, in thelimiting case where the waveguide possesses vertical symmetry (e.g.,FIG. 2, where t=h), then the Brillouin-active modes can converge tosymmetric Lamb waves with nearly identical dispersion curves to thosepresented in FIG. 16. FIG. 16, is a representation of an optical wavevector mismatch, Δk, produced by the dispersion of the optical waveguidemode, ω(k), as pump and Stokes waves are detuned. Accordingly, the wavescan be classified as symmetric Lamb waves, producing equal frequencyspacing of the phase-matched Brillouin modes, as shown in FIG. 15.

Full-vectorial multi-physics simulations based on waveguide device 100were performed and conveyed the elastic wave motion for sevencharacteristic Brillouin-active phonon modes. Periodic boundaryconditions were applied to the z-normal faces of the simulation domainsof FIGS. 17-23 to facilitate capture of the nature of a respectivetravelling-wave for the guided phonons at the phase-matched K-valuesidentified in FIG. 15. Accordingly, FIGS. 17-23 present sevencharacteristic Brillouin-active phonon modes, m=1-7 at respectivefrequencies 1.28, 3.72, 6.18 GHz, etc. As previously mentioned, in anaspect, the phonon modes presented in FIGS. 17-23 can be consideredcorresponding to symmetric Lamb waves.

Based upon the foregoing, a waveguide device 100 was formed with aseries of 26 reflector pairs (e.g., 26 pairs of slots 150 and 155) alongthe path traversed by an optical waveguide 130, to facilitate formationof a Brillouin-active length of 3.3 mm in a total device length of 4.9mm. In an aspect, a 3.3 mm Brillouin-active device length coincides witha total non-linear phase mismatch, |ΔK|·L, of between 0.45 and 5.7radian for the range of Brillouin-active modes presented in FIGS. 17-23.In an embodiment, each suspended waveguide section (e.g., a length ofwaveguide core 130 that has an adjacent slot 150 and 155) is separatedby a 25 μm anchored (or unsuspended) region, as indicated by FIG. 3,region M. In an embodiment, waveguide device 100 produces a significantnon-linear phase mismatch along its length. Hence, the variousembodiments relating to waveguide device 100 can be treated as aphase-matched travelling-wave process to facilitate describing thecoherent addition of non-linearities along the entire length of thewaveguide 130 in waveguide device 100.

A plurality of waveguide devices 100 have been studied with waveguidewidths, w, ranging from 0.8-3.8 mm, which produced a range of Brillouinresonances over a frequency range of 1-18 GHz. As an optical groupvelocity, ν_(g), changes by only a few percent over a 30-nm wavelengthrange, the optical phase mismatch (with values, |ΔK|·L≦2π) can havenegligible change over an appreciable wavelength range. Accordingly, thesame guided phonon can be excited by continuum of different wavelengthswithin the waveguide device 100, even though the waveguide device 100can operate as a phase-matched non-linear process. Such operationenables waveguide device 100 to operate with pump and probe waves ofdisparate wavelengths to couple to each other through theBrillouin-active modes of a single waveguide device 100.

To facilitate further understanding, FIG. 24 presents data derived fromtesting of a waveguide device 100, wherein, as previously mentioned, thewaveguide device 100 was formed to comprise 26 reflector pairs (e.g.,slots 150 and 155) along the path traversed by an optical waveguide 130,to facilitate formation of a Brillouin-active length of 3.3 mm in atotal device length of 4.9 mm. Experimental studies of a Brillouinnon-linearity were performed with a heterodyne FWM apparatus,facilitating direct measurement of the third-order non-linearsusceptibility. During the FWM experiments, a modulated pump signal(e.g., 1,556 nm) and continuous-wave probe signal (e.g., 1,536 nm) areinjected into a waveguide 130 of waveguide device 100. The modulatedpump signal can drive the excitation of Brillouin-active phonons over awide range of frequencies as the pump modulation frequency is sweptthrough a range of values. The non-linear response of the waveguidedevice 100 can be subsequently analyzed by heterodyne measurement ofoptical tones imprinted on the disparate probe wavelength as a result ofa coherent combination of the Brillouin and third-order electronicnon-linear susceptibilities (e.g., through FWM). Any signal sidebandscan then be analyzed as distinct RF tones through heterodyneinterferometry. Such an approach enables the Stokes and anti-Stokessignatures to be resolved separately.

As presented in FIG. 24, signatures showing a non-linear Brillouinresponse can be observed by measuring an intensity of non-linearlyinduced sidebands imprinted on a probe signal, as the frequency of apump modulation signal was swept from 1 to 18 GHz. The spectra in FIG.24 were obtained by integrating the RF power produced by heterodynedetection of a probe signal (including both Stokes and anti-Stokessidebands) over a discrete set of high-frequency RF bands using RFfilters. To remove the frequency dependence of the detection system andto more clearly exhibit the sharp Brillouin resonances, the spectra inFIG. 24 were normalized to those of an identical optical waveguidewithout a Brillouin-active region. Each waveguide produces a series ofregularly spaced Brillouin resonances analogous to those identified inFIGS. 17-23.

Owing, in part, to a spatial symmetry of the optical force distribution,only phonon modes with even displacement symmetry, with respect to thewaveguide core 130, produce efficient Brillouin coupling. A total of 17resonances are presented in FIG. 24, where each respective resonancefrom 1 a, 1 b, . . . 2 a, 2 b, . . . 7 a, is connected by mode orderplots, where: plot 2410 is mode m=1, plot 2420 is mode m=2, plot 2430 ismode m=3, plot 2440 is mode m=4, plot 2450 is mode m=5, plot 2460 ismode m=6, and plot 2470 is mode m=7, to indicate the mode order of eachphononic resonance as the Brillouin spectrum shifts with waveguidedimension.

As shown in FIG. 24, four waveguide devices 100 are presented withrespective waveguide dimension width d, where plot 2480 d=0.8 μm, plot2482 d=1.8 μm, plot 2484 d=2.8 μm, and plot 2486 d=3.8 μm, where width dis the phononic distance between two opposite slits (e.g., slits 150 and155), as shown in FIG. 8. The 17 resonances are observed as thefrequency is swept between 1 and 18 GHz.

As shown, plots 2410-2460 are also simulated mode frequencies over therange of device dimensions, and good agreement occurs between theobserved resonances and the anticipated values (e.g., an anticipatedvalue occurring where a mode plot 2410-2460 intersects a waveguidedimension plot 2480-2486).

FIG. 24 illustrates that a variation of the cavity dimension (e.g.,width d) enables precise placement of Brillouin resonances at anyfrequency from 1 to 18 GHz, with a high degree of non-lineartailorability. For example, the m=2 resonance (plot 2420) is shiftedfrom about 3.7 to about 17 GHz, as the cavity dimension, d, is variedfrom 3.8 μm to 0.8 μm. It is to be noted that while bandwidthlimitations of the testing apparatus did not permit measurements beyond18 GHz, strong Brillouin resonances are expected at 50 GHz and higherfrequencies.

With further reference to the resonance signatures presented in FIG. 24,a Fano-like line shape can be seen to be produced by each Brillouinresonance, from which the magnitude of the Brillouin non-linearcoefficient, γ_(SBS), can be obtained. The Fano-like line shape can beseen in the high-resolution spectral scans of FIGS. 25 and 26, whichshow the line shape of a characteristic Brillouin resonance (f=6.185GHz, with d=3.8 μm) decomposed into its Stokes (e.g., FIG. 25) andanti-Stokes (e.g., FIG. 26) components. The data presented was obtainedby spectrally resolving distinct heterodyne tones of the Stokes andanti-Stokes signals using a high-resolution RF spectrum analyzer as thepump modulation frequency was swept from about 6.16 GHz to about 6.2GHz. The asymmetric line shapes shown in plots 2510 and 2610 result fromthe coherent interference between the Brillouin and electronic Kerrnon-linearities of the waveguide device 100. Involvement of electronicKerr non-linearities at the Stokes and anti-Stokes frequencies can occurdue to cross-phase modulation between a pump beam and a probe beampropagating in the silicon waveguide core 130.

To facilitate determination of the magnitude of the Brillouin nonlinearcoefficient, γ_(SBS), relative to the intrinsic Kerr non-linearcoefficient γ_(K) and the non-linear free-carrier dispersion coefficientγ_(FC) from the data presented in FIGS. 24, 25, and 26, non-linearcoupled amplitude equations were formulated to derive the functionalform of the Stokes and anti-Stokes line shapes. The equations arepresented herein as Eqns. 1a-7 below, accompanied with explanatory text.

Owing to SBS being a resonant effect, a SBS non-linear coefficient canform a Lorentzian line shape centred about each Brillouin-active phononmode. In contrast, the electronic Kerr non-linearities are nonresonantat 1,550 nm wavelengths, yielding a frequency-independent non-linearcoefficient. As is known in the art, the frequency-dependentinterference between the Kerr and Brillouin effects can produce theasymmetric (e.g., Fano-like) line shape, as shown in plots 2510 and2610. However, it should be noted that the experimental arrangementutilized to measure the values presented in FIGS. 24-26 is distinct,leading to a different set of coupled amplitude equations. In addition,non-linearly generated free carriers in Si can be responsible for thedissimilar line shapes of the Stokes and anti-Stokes orders, and alarger nonlinear background for frequencies below 2 GHz under theexperimental conditions utilized herein. As the free-carrier effectsroll off at high frequency, the Kerr responses at 16 GHz are used as areference to determine the magnitude of the Brillouin non-linearcoefficient.

On the basis of the coupled amplitude model described with reference toEqns. 1a-7, the magnitude of the Brillouin non-linear coefficient,γ_(SBS), can be extracted from the experimental line shape of both theStokes and anti-Stokes signatures of each resonance of the waveguidedevice 100 having a width d=3.8 μm.

Seven resonances, spanning frequencies from 1.28 to 16.30 GHz, are shownin FIG. 27. The peak value of |γ_(SBS)|/|γ_(K)| and the phononicQ-factor of each resonance extracted from experiments (includingseparately resolved Stokes and anti-Stokes signatures) are shown FIGS.29 and 30 respectively. The peak value of the Brillouin non-linearcoefficient at 1.28 GHz is found to be 6.18 times larger than the Kerrnon-linear coefficient of the waveguide (or |γ_(SBS)|/|γ_(K)|=6.18).

From the established non-linearities of Si, |γ_(K)| of 188±34 W⁻¹ m⁻¹were determined for a waveguide device 100 with w=[1.8, 2.8, 3.8] μm(per Eqns. 1-7 herein). From this relative measurement, the Brillouinnon-linear coefficient is found to be |γ_(SBS)|≅1.164±244 W⁻¹ m⁻¹ overthe Brillouin-active region of the waveguide device 100. Moreover, asthe Brillouin non-linear coefficient is related to the Brillouin gain as2 |γ_(SBS)|=G_(SBS), this nonlinearity corresponds to a forward SBS gainof G_(SBS)≅2,328±488 W⁻¹ m⁻¹.

It is to be noted that much of the ±18% and ±21% uncertainty assigned to|γ_(SBS)| and |γ_(K)| values, respectively, can arise from the (±15%)uncertainty in the measured value of the Kerr non-linearity for silicon.Despite the fact that this non-linear response is the aggregate of anensemble of 26 distinct Brillouin-active suspended regions fabricatedalong the length of the waveguide device 100 as previously described,high mechanical Q-factors (˜1,000) are produced for phonon frequenciesof about 1.28 to about 16.3 GHz.

For comparison with experiments, full vectorial three-dimensionalmulti-physics simulations were performed through coupled optical forceand elastic wave finite element analysis and simulation models. Thedistinct contributions of ES forces (plot 2810, orange), radiationpressure (plot 2820, blue) and thermoelastic expansion to the total SBSnonlinear coefficient (plot 2830, black) are shown in FIG. 28 for eachphonon resonance mode m=1-7. A fixed mechanical Q-factor of Q=1,000 isassumed. Note that negligible contribution to the Brillouin coupling isproduced by thermoelastic response at these GHz frequencies due to, atleast in part, the slow thermal time constant of this system (forfurther details, refer to Eqns. 1-7 and accompanying text). Themagnitude of the Brillouin coefficient, |γ_(SBS)|, scales quadraticallywith optical force, yielding a non-linear addition of the radiationpressure and electrostrictively induced couplings to the overallBrillouin gain as shown in FIG. 28. The total Brillouin non-linearity,which is almost exclusively driven by radiation pressure andelectrostriction, slowly decreases with increasing resonant frequency asfurther shown in FIG. 28.

A larger variation in Brillouin non-linearity is seen from theexperimental data (e.g., circles of FIG. 29) than from simulations(e.g., 2830, black bars of FIG. 28) due to the variation of the measuredphononic Q with frequency (per FIG. 30). However, when the frequencydependence of measured Q-factors is included in simulations (per FIG.30), good agreement between simulations and experiments are obtainedover the entire frequency range, per the green bars and the circles ofFIG. 29.

Both the highly localized electrostriction and radiation pressure forcedistributions within a waveguide core 130 yield a frequency dependentBrillouin gain (as shown in FIG. 28) exhibiting a significant departurefrom conventional backwards SBS processes involving bulk acoustic waves.In contrast to the rapid 1/Ω roll off of Brillouin gain with phononfrequency found through backward SBS, the experimental (and simulated)Q-factor normalized Brillouin coefficient varies by less than 40% inmagnitude over the entire 1-16 GHz frequency range.

Unlike conventional systems where the overlap between the optical forcedistribution and the phonon mode profile is largely frequencyindependent, the complex double-lobed spatial force distributions in thecore of the silicon waveguide 130 can produce a frequency dependentoverlap with various phonon modes, reshaping the frequency dependence ofBrillouin coupling. The effect of spatial force distribution on thefrequency dependence of coupling can be seen by comparing the computedcontributions of electrostriction and radiation pressure to theBrillouin gain of FIG. 28. Although the radiation pressure contributiondiminishes quite rapidly with frequency, the ES component varies by onlya few percent over the 1-16 GHz frequency range. The higher bandwidth ofES coupling can result from the higher spatial frequencies of the ESforce distribution. Consequently, the relatively flat Brillouin gainproduces efficient photon-phonon coupling over an unprecedentedfrequency range.

The magnitude and frequency dependence of the measured Brillouincoupling, and the good agreement with simulations, all provide strongevidence of the important role of both electrostriction and radiationpressure within the waveguide devices formed in accord with the variousembodiments presented herein.

The series of Brillouin resonances generated by a waveguide device 100having d=3.8 μm can provide insight into the bandwidth and frequencydependence of the Brillouin coupling.

However, a larger overall Brillouin non-linearity can be achieved with ahigher degree of phonon confinement, that is, for smaller values of d.FIG. 31 shows the Stokes and anti-Stokes spectral line shapes obtainedby through-measurement of the d=0.8 μm waveguide device 100. In contrastto the d=3.8 μm device, several sharp spectral features, consistent withhigh Q-factor (Q˜1,500) phononic resonances, are observed within thecentral Brillouin line shape, suggesting significant inhomogeneousbroadening which may be due to fabrication non-uniformities.

A fit of the aggregate Brillouin line shape using a single Lorentzianoscillator model yields is seen in FIG. 31, yielding G_(SBS) andQ-values of G_(SBS)≅4,150±872 W⁻¹ m⁻¹ and Q≅280. However, uncertainty inthe form of inhomogeneously broadened line shape made it difficult toobtain a high confidence estimate of the Brillouin non-linearity in thiscase, prompting exploration for Brillouin non-linearities through directmeasurement of Brillouin gain.

Experimental studies of Brillouin gain were performed by injectingstrong pump and weak signal fields into a Brillouin-active waveguide(w=0.8 μm). A low spectral-intensity amplified spontaneous emission(ASE) probe signal (centre wavelength: 1,552.94 nm; bandwidth: 50 GHz)was used in conjunction with a high-intensity pump laser(λ_(p,AS)=1,552.723 nm or λ_(p,AS)=1,553.158 nm) to perform Brillouingain measurements about the Stokes and anti-Stokes frequencies,respectively. The spectral power density of the ASE signal beam wasmeasured by monitoring the heterodyne interference between the pump andsignal fields with a receiver and a RF spectrum analyzer (SA) forfrequencies about the Brillouin resonance (e.g., v=5.68 GHz).

The transmitted ASE power spectral density for higher pump powers arenormalized to the power spectral density at lower pump powers (e.g.,about 2.6 mW) to observe the power-dependent form of the Stokes andanti-Stokes line shapes. The normalized Stokes and anti-Stokestransmittances for P_(p)=12, 14 and 20 mW are shown in FIGS. 32 and 33respectively. The finer structure produced by inhomogeneous broadeningis not visible owing to the smaller signal-to-noise ratio obtained bythis method.

Lorentzian fits of the Stokes and anti-Stokes line shapes yield aQ-factor of approximately 300, indicating significant inhomogeneousbroadening. As the anti-Stokes process involves transfer of energy fromthe signal to the pump beam, the anti-Stokes signature (as shown, e.g.,in FIG. 33) exhibits depletion instead of gain as shown in FIG. 32.

In FIGS. 31-34, theoretical line fitting curves are indicated inconjunction with experimental data, presented in the form of circles. Inthe small signal limit, which is explored in the experiments, the SBSgain is proportional to the pump power, and the amplification (and alsodepletion) at resonant center frequency is linear with the pump power asshown in FIG. 34. A total effective forward SBS gain ofG_(SBS)≅2,750±1,200 W⁻¹ m⁻¹ was extracted by fitting the data in FIGS.32 and 33. This measurement also shows good agreement with the simulatedvalue of Brillouin gain, G_(SBS)≅2,750±540 W⁻¹ m⁻¹. It is to be notedthat the derived values for Brillouin gain are more than a factor of 10larger than those obtained by treating the Brillouin non-linearities ofSi as a bulk medium property, which accordingly, provides strongevidence of the role of boundaries in shaping non-linearity atsub-wavelength scales.

The previously presented measurements demonstrate a gain coefficientthat is over 1,000 times larger than forward SBS obtainable in aconventional system such as waveguide fibers, and several times largerthan the Raman gain produced by Si, making Brillouin non-linearities thedominant third-order non-linearity in the waveguide device 100, inaccord with the various embodiments herein.

In accord with the various embodiments presented herein, travelling-waveBrillouin non-linearities and Brillouin gain in waveguide device 100through a novel class of hybrid photonic-phononic waveguides are furtherdescribed. Through quantitative measurements, forward SBS non-linearsusceptibilities were measured to be more than one thousand timesstronger than a conventional waveguide system. Multi-physics simulationsreveal that this strong photon-phonon coupling is produced by aconstructive combination of ES forces and radiation pressures at thenanoscale. The emergence of large radiation pressure-induced couplingsrepresents a new form of boundary-induced Brillouin non-linearity and anew regime of boundary-mediated Brillouin coupling that arises insubwavelength structures.

The embodiments presented herein enable independent control of phononicmodes and optomechanical driving forces to yield tailorable Brillouincoupling over exceptionally wide bandwidths. Simultaneous coupling tonumerous transverse phonon modes yields a relatively flat Brillouin gainover this entire 1-18 GHz frequency range. Further, structural tuning ofphononic resonances from 1 to 18 GHz with high-quality factor (41,000)yields tailorable non-linear optical susceptibilities due to thecoherent interference of Kerr and Brillouin effects.

Further, the various embodiments presented herein indicate a widebandnature of the photon-phonon coupling results from the highly localizedoptical forces produced within the nanoscale waveguide device 100. Thewideband and high-frequency (1.g., about 18 GHz) characteristics can beachieved without a requirement for ultra-high resolution lithography,significantly extending the frequency range of chip-scale photon-phononcoupling over conventional cavity optomechanical technologies.

Efficient coupling between a continuum of optical and phononic modesthrough such chip-scale travelling-wave Brillouin processes facilitatesapplication in a range of technologies utilizing widebandsignal-processing capabilities with CMOS-compatible silicon photonics,including pulse compression, pulse and waveform synthesis, coherentfrequency comb generation, variable bandwidth optical amplifiers andfilters, and coherent beam-combining schemes. Travelling-wave Brillouinnon-linearities can also produce optical phase conjugation andopto-acoustic isolators for application in reducing signal distortionand eliminating parasitic reflection on silicon chips. In addition, thehighly controllable nature of the phonons emitted by the waveguidedevices presented herein operating as a hybrid photonic-phononic systemcan facilitate forms of coherent information transduction throughtravelling-wave processes that are complementary to conventional cavityoptomechanical systems.

As efficient Brillouin-based photon-phonon conversion is possible overwide bandwidths (>20 GHz), and the Brillouin-emitted phonons can beguided and manipulated on chip, hybridization of Brillouin devicephysics with silicon photonics, CMOS and microelectromechanical systemscan provide a host of new coherent signal-processing technologies.

It is to be appreciated that the dimensions and frequency bandspresented above are to be understood as merely exemplary and notlimiting. For example, the spacing of the air slots 150 and 155 may beas small as the width of the optical waveguide 130, and may be as greatas 20 μm or more, as may be permitted by the mechanical strength of themembrane 140. In an aspect, degradation in the resonant behavior of thephononic resonators does not appear to be a limiting factor, as thequality factor of the resonator is only weakly dependent, if at all, onthe width of the resonator. Hence, device 100 and similarly formeddevices, can be effective over a bandwidth as great as 100 MHz to 50GHz, or even more. Further, the optical waveguide device 100 can befabricated with a width d of 2.0 μm, or higher.

As previously mentioned, membrane 140 can act to confine the generatedphonons. As shown in the phase matching diagrams of FIGS. 12-14, aforward-SBS process phase-matches to phonons with a vanishinglongitudinal wave-vector (i.e. slow group-velocity guided phononstates). Hence, at least for certain applications, it might be necessaryto engineer high Q-factor phononic resonances that support modes oflarge transverse wave-vector (i.e. perpendicular to the waveguide). HighQ-factor phononic resonances can be achieved by truncating the membrane140 on either side of the waveguide 130 with etched air-slots 150 and155 (e.g., of dimension 2×100 μm), per the structure shown in FIGS. 1-4.The slots 150 and 155 can act to reflect acoustic waves, which canfurther define the extended phonon modes. This geometry, which can betermed, produces efficient photon-phonon coupling over a series ofdiscrete phononic resonances between 1-18 GHz, through a traveling-waveforward-SBS process.

Numerous variations on the layout described above with reference towaveguide device 100 are possible and are considered to fall within thescope of the various embodiments presented herein. For example, the airslots 150 and 155 may be replaced by reflective features of other kindsOne such alternate reflective feature is a phononic crystal, defined,e.g., by a two-dimensional array of holes etched through the membrane.Another alternate type of reflective feature is a Bragg grating. FIG. 35presents a waveguide device 3500, where the slotted reflectors of device100 are replaced with an array of holes 3570 and 3580 (e.g., a pair ofphononic crystals) located on either side of a waveguide core 130. Holes3570 and 3580 can be formed in a membrane layer 3540 which can be formedover a cavity 3560, which has been formed in an insulating layer 3520 ona substrate 3510. As per device 100, the respective components of device3500 can be formed from materials such as Si (e.g., substrate 3510 andwaveguide core 3530), SiO₂ (e.g., insulating layer 3520) and Si₃N₄(e.g., membrane 3540).

In an aspect, compared with a slot reflector (e.g., slots 150 and 155)device, a device formed with phononic crystal mirrors (hole arrays 3570and 3580) can facilitate controllable (tailored) leakage (or coupling ofenergy) from a waveguide core (e.g., waveguide core 3530). Thecontrollable leakage (e.g., across a resonance frequency range of about1-20 GHz) can facilitate resonant transfer of information (or phonons)between waveguides in the absence of optical energy transfer. Further,phononic crystal waveguides 3500 can be fabricated with longer phononicresonator regions than can be formed with a slot waveguide device. Thiscan eliminate the problem of anchoring losses for the phonons whichoccurs with slot waveguide devices (e.g., as can occur at region 190).

In other embodiments, the reflective features 150 and 155 of device 100can have a disposition that is not symmetric about the optical waveguide130. For example, as shown in FIG. 36, a pair of optical waveguides 3630and 3635 can be formed in a waveguide device 3600. Waveguides 3630 and3635 can be disposed parallel to each other and sufficiently near eachother to be optically coupled, whereby the coupling can be by a phononicregion 3690 located between waveguides 3630 and 3635. Accordingly,rather than optical-cross talk coupling the waveguides 3630 and 3635,the coupling is phononic.

In a conventional approach, if two signals are transmitted down a singlewaveguide, undesirable cross-talk can occur between the two signalwavelengths owing to non-linearities that may be present. Such anundesirable interaction can occur in Si waveguides. However, byutilizing two separate waveguides 3630 and 3635, each respective signalin each waveguide can communicate with the other signal via the phonons.Accordingly, a pure communication can occur between the two waveguides3630 and 3635, with narrow resonances available through which thewaveguides 3630 and 3635 can transfer information.

In an embodiment, the dual waveguide device 3600 is amenable to narrowacoustic or phononic resonance which can act as an optical filter as theresonances can be in the order of 1 MHz wide. Such narrow or acousticresonance can be particularly useful for radio frequency signalprocessing and filtering.

In an illustrative scenario, a pump signal P_(in) is injected intowaveguide 3630 in conjunction with a modulated information signal M_(in)which carries the signal information. Accordingly, P_(in) and M_(in) canbeat together, with the information in M_(in) being transduced as afunction of the beat note. In the second waveguide 3635, a continuouslight beam S_(in) can be injected. As light beam S_(in) passes throughthe waveguide 3635, side bands can be developed, whereby the sidebandscan be affected by the transduction, originating in waveguide 3630, andbeing carried over region 3690. Accordingly, information comprisingM_(in) can be carried over to the S_(in) beam leading to S_(in) beingmodified to a beam SM_(out), whereby SM_(out) includes informationtransferred over from M_(in).

In another embodiment, a waveguide device can be formed with confocalresonators. For example, as shown in FIG. 37, a waveguide device 3700can be formed comprising a pair of confocal resonators 3750 and 3755formed in membrane 3740. Accordingly, the confocal resonators 3750 and3755 can act to focus phonons at a central region 3790 located inresonator regions 3770 and 3780 operating adjacent to waveguide core3730.

In further embodiments, phononic resonators as described above can betraversed by an optical waveguide that is curved and not straight. Forexample, a Brillouin laser may include an optical resonator thatconsists of an optical waveguide conformed in a closed curve such as acircle, dimensioned to resonate at a Stokes-shifted oranti-Stokes-shifted pump frequency, and disposed on a path thattraverses one or more phononic resonators. When excited by pumpradiation introduced, e.g., by optical coupling from an adjacentwaveguide, the optical resonator may exhibit gain at the resonantfrequency, thus producing amplified Stokes or anti-Stokes radiation.Similar arrangements may serve as optical amplifiers, optical filters,and the like. For example, a Brillouin waveguide can facilitateamplifying a weak signal, when in the presence of a pump signal, to forman amplified output signal.

Those skilled in the art will appreciate that depending on theapplication, any of the various inputs to such a system may be deemedthe signal input, and likewise any of the various outputs may be deemedthe signal output. Hence, a system similar to the measurement systempreviously described can operate to produce an output optical signal inresponse to an input optical signal, an output optical signal inresponse to an input RF signal, an output RF signal in response to aninput optical signal, or an output RF signal in response to an input RFsignal.

In the system described above, RF modulation can be utilized to excitethe phonons. On the other hand, phononic excitation may occur without RFmodulation in systems that exhibit gain at the Stokes or anti-Stokesfrequency. One such example is provided above, i.e. the Brillouin laserusing a ring resonator, i.e., a circular resonant waveguide. As shown inFIG. 38, a waveguide device 3180 can be utilized in conjunction with acircular resonant waveguide 3870. A pump laser 3820 and a signal laser3830 can be utilized to generate respective pump signals 3840 andsignals 3850 which can be transmitted into a waveguide 3860. Waveguide3860 can be coupled to the circular resonant waveguide 3870, wherebyBrillouin SBS can occur between the circular resonant waveguide 3870 andwaveguide 3860. Based upon the combination of coupling and BrillouinSBS, the output signal 3890 can be delayed with respect to the laserpump signal 3880. In a further example that operates on similarprinciples, the ring resonator is omitted and instead, the resonantcavity can be defined by a pair of Bragg gratings formed in the opticalwaveguide traversing the phononic resonators.

FIGS. 39-44 present stages in a fabrication process which can beutilized to form a waveguide device such as devices 100, 3700, 3800,3900 or 4000. As shown at FIG. 39, a substrate 110 can be formed, wherethe substrate can comprise silicon. Formed thereon is an insulatinglayer 122, where the insulating layer can comprise SiO₂. A second layer132, comprising Si, can be formed on insulating layer 122, with a resistlayer 195 formed to facilitate patterning to form the waveguide 130. Inan embodiment, the waveguide device 100 can be considered to comprise asilicon-on-insulator substrate with a 3000-nm oxide undercladding.

As shown in FIG. 40, a process of deep ultraviolet (UV) lithography, adeep silicon etch (DPS) followed by a resist strip, a standardpost-etch, and a pre-diffusion clean, can facilitate formation of awaveguide 130 on the surface of the insulator layer 122.

Any suitable process can be utilized to form a Si₃N₄ layer, as shown inFIG. 41. Such a process can include a low pressure chemical vapourdeposition (LPCVD) operation. The nitride layer 142 is deposited on theexposed surface of the insulating layer 122 and also over the waveguide130, where in an example embodiment, nitride layer 142 can be 300 nmthickness.

In FIG. 42, a chemical-mechanical polish (CMP) can be performed topreferentially thin the conformal nitride layer atop the waveguide 130.A wet etch, such as hot phosphoric acid etch can also be utilized toclear any remaining nitride atop the waveguide 130.

FIG. 43 presents the result of the CMP and cleaning operations. A deepUV lithography operation in conjunction with an etch operation (e.g., aplasma etch) can be utilized to form openings 148 in resist layer 196,and nitride layer 140. The openings 148 can ultimately form air slots150 and 155. An etch operation (e.g., 49% HF etch with Tergitol) can beutilized to form a hollow region beneath the nitride layer 140.

FIG. 44 presents a final structure (e.g., waveguide device 100)comprising a substrate 110, support structures 120, with a membranelayer 140 formed over the opening 160. The membrane layer 140 isattached to the waveguide core 130 and further includes slots 150 and155.

It is to be appreciated that while the foregoing embodiments (e.g.,devices 100, 3500, 3600, and 3700) have presented devices where thewaveguide core (e.g., waveguide core 130) is formed from a differentmaterial from that used for the resonator membrane (e.g., layer 140),other embodiments are envisaged in which the waveguide core and themembrane layer are formed from the same material. For example, FIG. 45presents a scanning electron micrograph of a dual photonic crystalwaveguide device 4500, wherein the waveguide cores and membranes areformed from the same material, e.g., Si. As shown in FIG. 45, waveguidedevice 4500 includes two waveguide cores 4530 and 4540 formed in thesame layer as membrane 4510 and phononic crystal regions 4250. Waveguidecores 4530 and 4540 are located between a plurality of slots 4550 formedin membrane 4510, whereby the slots 4550 can act to constrain lightand/or acoustic waves in the waveguide cores 4530 and 4540.

However, in contrast to the step-index waveguides (e.g., devices 100,3500, 3600, and 3700) which guide light and/or acoustic waves by totalinternal reflection (e.g., in waveguide core 130), waveguide 4500 canguide light and/or acoustic information as a consequence of Braggreflection through the formation of an optical bandgap.

As shown in FIG. 46, if a pump signal Pp is injected into a firstwaveguide 4540 at a frequency of less than about 8 GHz a conversionefficiency is minimal, even impaired, as shown in FIG. 48, region 4810,with no interaction occurring with the probe beam Pr (e.g., Pr remainsflat). In an embodiment, a transmission of energy in the pump signal Ppcan be of an ultra-wideband stimulated Mach-wave emission, e.g., acrossa frequency range of 2-11 GHz. Further, the pump signal Pp can beconstrained in the first waveguide 4540 based upon Bragg reflectionoccurring at the phononic crystal regions 4520. Effectively, thephononic crystal regions act to confine the Pp signal as a function ofelectrorestrictive forces generated as a result of an optical mode ofthe Pp signal interacting with the phononic crystal regions 4520, e.g.,a phononic defect mode. Owing to the Mach-wave emission, at a frequencyof less than about 8 GHz (e.g., a frequency below a phononic bandgap)any acoustic waves generated at the first waveguide 4540 propagatefreely across all of the phononic crystal regions 4520.

However, as shown in FIG. 47, when the pump signal Pp is injected intothe first waveguide 4540 at a frequency of the phononic bandgap (e.g.,of about 8-9.5 GHz, as shown, e.g., in FIG. 48, region 4820), anyinformation in the pump signal Pp can be resonantly coupled to the probebeam Pr injected into the second waveguide 4530. Hence, when operatingat a phononic bandgap frequency, the waveguide device 4500 can operateas a tunable reflector for sound (i.e. a phonic bandgap reflector) whilesimultaneously conveying signal Pp along the first waveguide 4540. Thewaveguide device 4500 can effect efficient transfer (as shown in FIG.48) of energy over a narrow bandwidth(s).

As will be understood by those skilled in the art, one possible outputof a system such as that described above is a phase-modulated version ofthe probe beam. The phase modulation may be understood, in one sense, asresulting from changes in the refractive index created by the action ofthe pump radiation. This behavior can be readily utilized to create,e.g., an optical filter.

Other possible applications utilize an optical frequency comb, createdby cascaded Brillouin processes, i.e., by Stokes or anti-Stokes shiftsthat are repeated one, two, three, or more times. This may occur, forexample, in a Brillouin laser in which the free spectral range of theresonant cavity is divisible by the phonon frequency. Because theresulting comb lines are coherent, it might be possible to use such acascaded process to generate optical pulses.

In other possible applications, the probe beam can be split andsimultaneously injected into a plurality of optical waveguides, all ofwhich traverse phononic resonators and all of which are acousticallycoupled via the suspended membrane. A pump beam injected into one ormore designated driver waveguides generates phonons that propagatethrough the membrane and locally excite the resonators traversed by therespective optical waveguides at different times determined by therespective phononic propagation delays. The resulting frequency or phasemodulation of optical pulses injected via the probe beam can be utilizedto operate such an arrangement as an optical pulse delay circuit or anoptical pulse shaper.

In Brillouin laser applications, it may be possible to actively modelock the laser by modulating the pump beam at a desired pulse frequencythat is compatible, e.g., with a harmonic of the optical cavity roundtrip time and of the phononic cavity round trip time.

To facilitate understanding of the various embodiments presented herein,coupled wave equations are developed which describe the nonlinearwave-mixing processes which can occur in a waveguide device 100, andfurther, derive functional form of the various asymmetric line-shapesobserved through heterodyne pump-probe experiments. By utilizing theanalytically derived line-shapes, quantitative analyses of theexperimental signatures are performed to determine the magnitude of theBrillouin nonlinear coefficient.

As previously described, a function of the various geometries ofwaveguide devices 100 can facilitate mutually incoherent pump and probebeams being coupled into the Brillouin waveguide. A pump beam can beproduced by intensity modulation of a monochromatic laser line.Modulation at frequency Ω, generates a pump beam comprising twofrequencies, ω₁ and ω₂, with corresponding wave amplitudes A₁ and A₂,where ω₂−ω₁=Ω. A probe beam can comprise of a monochromatic wave havinga disparate wavelength to the pump beam, with wave amplitude A₃ andfrequency ω₃. Nonlinear wave-mixing processes involving A₁, A₂ and A₃generate Stokes and anti-Stokes fields at frequencies ω_(s)=ω₃−Ω, andω_(a)=ω₃+Ω, with a Stokes wave amplitude A_(s) and an anti-Stokes waveamplitude A_(a) respectively. The wave-amplitudes A_(s) and A_(a) can bemeasured through heterodyne detection to produce the line-shapespreviously discussed, e.g., with reference to FIGS. 24-34. Forsimplicity, it can be assumed that both pump and probe waves are coupledto transverse electric-like (TE-like) waveguide modes. Owing to theStokes and anti-Stokes waves having zero amplitude at the entrance towaveguide 130, the coupled wave equations for Stokes and anti-Stokeswave growth can, to first order, be expressed as:

$\begin{matrix}{\frac{\mathbb{d}A_{s}}{\mathbb{d}Z} = {{i\left\lbrack {{\gamma_{SBS}^{{(3)}^{*}}(\Omega)} + {2\gamma_{FWM}^{(3)}} + {{\gamma_{FC}^{(5)}\left( {- \Omega} \right)}P_{0}}} \right\rbrack}A_{1}^{*}A_{2}A_{3}}} & {{{Eqn}.\mspace{14mu} 1}a}\end{matrix}$

$\begin{matrix}{\frac{\mathbb{d}A_{a}}{\mathbb{d}Z} = {{i\left\lbrack {{\gamma_{SBS}^{(3)}(\Omega)} + {2\gamma_{FWM}^{(3)}} + {{\gamma_{FC}^{(5)}\left( {+ \Omega} \right)}P_{0}}} \right\rbrack}A_{1}A_{2}^{*}A_{3}}} & {{{Eqn}.\mspace{14mu} 1}b}\end{matrix}$

where, P₀=2(|A₁|²+|A₂|²+|A₃|²), and γ_(SBS) ⁽³⁾ and γ_(FWM) ⁽³⁾ are thethird order nonlinear coefficients for stimulated Brillouin scattering(SBS) and non-degenerate four-wave mixing (FWM), respectively. Inaddition, γ_(FC) ⁽⁵⁾(Ω) is the fifth order nonlinear coefficient whichresults from two-photon absorption (TPA) induced by free carrierabsorption and refractive index changes imparted by waves A₁, A₂ and A₃.In the above Eqns 1a and 1b, the two-photon absorption (TPA) inducedattenuation of A_(s) and A_(p) has been neglected, since in this smallsignal limit, these terms are much smaller than the source terms of Eqn.1a and Eqn. 1b.

It is assumed that the Brillouin nonlinearity, γ_(SBS) ⁽³⁾(Ω), isdescribed by a single oscillator, yielding a Lorentzian line-shape ofthe form:

$\begin{matrix}{{\gamma_{SBS}^{(3)}(\Omega)} = {\frac{G}{2}\frac{{\Omega_{m}/2}\; Q}{\Omega_{m} - \Omega - {i\;{\Omega_{m}/2}\; Q}}}} & {{Eqn}.\mspace{14mu} 2}\end{matrix}$

where, Ω_(m) is the resonant frequency of the m^(th) mode, Q indicatesthe quality factor of the phonon resonator, and G=2|γ_(SBS) ⁽³⁾(Ω)| isthe Brillouin gain. Solving for time-harmonically modulated TPA-inducedfree carrier generation rate, and using the carrier rate equation tosolve for γ_(FC) ⁽⁵⁾(Ω):

$\begin{matrix}{{\gamma_{FC}^{(5)}\left( {\pm \Omega} \right)} \equiv {{- \left( {\frac{M}{\tau} \pm \frac{V\;\Omega}{2}} \right)}\frac{1}{{1/\tau^{2}} + \Omega^{2}}}} & {{Eqn}.\mspace{14mu} 3}\end{matrix}$

where M and V are constants with positive value, and τ is the freecarrier lifetime. It is to be noted that γ_(FWM) ⁽³⁾ is wellapproximated as a frequency independent constant which can be computedfrom the waveguide geometry and a nonlinear coefficient of Si. Thus, inan aspect, FWM is non-dispersive, while Brillouin-induced couplings andthe free carrier induced nonlinear couplings can have frequencydependent responses in the example frequency sweeping range (e.g., 1-18GHz).

To remain consistent with the experimental arrangements, it is to benoted that the FWM and free-carrier effect occur through the waveguideentire waveguide length (e.g., a length of 4.9 mm), while theBrillouin-active interaction length is shorter than the total waveguidelength (e.g., a length of 2.6 mm). In such a scenario, the optical powerof the Stokes field obtained by solving Eqn. 1a is:g _(s) =C|γ _(SBS) ⁽³⁾*(Ω)L _(SBS)+(2γ_(FWM) ⁽³⁾+γ_(FC) ⁽⁵⁾(−Ω)P ₀)L_(tot)|² P ₁ P ₂ P ₃  Eqn. 4

where C is a constant, P_(k) indicates the optical power of k^(th)field, and L_(SBS) and L_(tot) are the interaction lengths of SBS andthe rest nonlinear responses, respectively. Eqn. 4 consists of twoterms, one for Brillouin scattering and another which includes bothnon-degenerate four-wave mixing (FWM) and free carrier effects. Thesignal from FWM and free carrier effect is referred to as the referencesignal. In the absence of the Brillouin nonlinearities (e.g., for largedetuning from a Brillouin resonance) the free carrier and FWMcontributions to the Stokes sideband can be described by:g _(os) =CL _(tot) ²|2γ_(FWM) ⁽³⁾+γ_(FC) ⁽⁵⁾(−Ω)P ₀|² P ₁ P ₂ P ₃  Eqn.5

Since the free carrier effects engender a slow variation across afrequency envelope, γ_(FC) ⁽⁵⁾(Ω) can be treated as a constant in thevicinity of a single Brillouin resonance (e.g. for frequency spans ofless than 100 MHz). Further, owing to γ_(FC) ⁽⁵⁾(Ω)≠γ_(FC) ⁽⁵⁾(Ω) fromEqn. 3, the reference signals for Stokes and anti-Stokes are expected todiffer from each other when Ω is comparable with 1/τ.

By fitting Eqn. 4 to the experimentally obtained Stokes and anti-StokesBrillouin scattering signals as shown in FIGS. 27 and 28, it is possibleto estimate the Brillouin gain, G=2|γ_(SBS) ⁽³⁾(Ω_(m))|. The normalizedfitting function g_(s)/g_(os) can be derived from Eqns. 4 and 5, toform:

$\begin{matrix}{\frac{g_{s}}{g_{os}} = {{{\mathbb{e}}^{{\mathbb{i}}\; b_{s}} + {D_{n}\frac{{\Omega_{m}/2}\; Q}{\Omega_{m} - \Omega - {i\;{\Omega_{m}/2}\; Q}}}}}^{2}} & {{Eqn}.\mspace{14mu} 6}\end{matrix}$

where D_(n)=GL_(SBS)/(2L_(tot)|2γ_(FWM) ⁽³⁾+γ_(FC) ⁽⁵⁾(−Ω)P₀|) is therelative strength of the Brillouin scattering effect relative to thereference nonlinear responses. Owing to γ_(SBS) ⁽³⁾(Ω) and γ_(FC) ⁽⁵⁾(Ω)being complex functions, the relative phase between the Brillouinscattering signal and background (FWM+FC) nonlinear responses is definedas b_(s) in Eqn. 6. The proportionality to P₁, P₂ and P₃ as well as theconstant C in Eqns. 4 and 5 are normalized out of Eqn. 6.

It is to be noted that owing to the frequency dependent free-carriereffect, different resonant modes are normalized by different nonlinearbackgrounds. In the previously described experiments, it was observedthat at high frequency (>15 GHz) the amplitude of the reference signalconverges to |2γ_(FWM) ⁽³⁾|, indicating |2γ_(FWM) ⁽³⁾|>>γ_(FC) ⁽⁵⁾(Ω)P₀.The reference signal spectrum can be measured to facilitate obtainingthe ration η≡|2γ_(FWM) ⁽³⁾+γ_(FC) ⁽⁵⁾(−Ω)P₀|/|2γ_(FWM) ⁽³⁾|. Byutilizing established methods for computing |2γ_(FWM) ⁽³⁾|, based onwell-known values for the Kerr nonlinearities of crystalline Si, anestimate of the Brillouin gain G can be determined according to thefollowing:

$\begin{matrix}{G = {2\; D_{n}\eta{{2\;\gamma_{FWM}^{(3)}}}\frac{L_{tot}}{L_{SBS}}}} & {{Eqn}.\mspace{14mu} 7}\end{matrix}$

It is to be noted that the propagation losses in Eqns. 1a and 1b do notappear in Eqn. 7, as losses do not alter the final functional form ofthe derived line-shape in the small signal limit.

The magnitude of γ_(FWM) ⁽³⁾ produced by the Si waveguide 130 wascomputed using an accepted Kerr coefficient of n₂=4.5×10⁻¹⁸[m²/W] forSi. Employing a full-vectorial method for computing γ_(FWM) ⁽³⁾according to conventional methodology, |2γ_(FWM) ⁽³⁾| is computed to be188 [1/W/m] for TOPROW waveguides with Si₃N₄ membrane widths of d=[1.8,2.8, 3.8] μm (WIDTH D of FIG. 4). As the Si₃N₄ width was reduced tod=0.8 μm, the close proximity of the lateral nitride boundary increasesthe modal confinement, yielding |γ_(FWM) ⁽³⁾| of 214 [1/W/m].

FIG. 49 is a methodology relating to phononic-photonic coupling in amembrane device. While methodology 4900 is shown and described as beinga series of acts that are performed in a sequence, it is to beunderstood and appreciated that the methodology is not limited by theorder of the sequence. For example, some acts can occur in a differentorder than what is described herein. In addition, an act can occurconcurrently with another act. Further, in some instances, not all actsmay be required to implement the particular methodology describedherein. At 4910, a first lightwave and a second lightwave can beinjected into a waveguide device, where the first lightwave has a firstfrequency and the second lightwave has a second frequency. As previouslydescribed, the waveguide device can include a waveguide along which thefirst lightwave and the second lightwave are transmitted, where thewaveguide can be formed in a membrane structure. Located on either sideof the waveguide can be a pair of slots which can act to bound aphononic resonator region respectively located on either side of thewaveguide.

At 4920, as a function of the first lightwave passing through thewaveguide, a combination of electrostrictive and radiationpressure-induced boundary forces can establish phononic activity in thephononic resonators.

At 4930, a phonon in the phononic resonator can propagate out in adirection substantially transverse to the waveguide optical direction.As the phonon propagates out, at a certain distance the phonon isincident upon a slot wall which can cause the phonon to be reflectedback to the waveguide, thereby generating one or more optical modes inthe phononic resonator, whereby the optical mode can be considered aform of vibration in the phononic resonator.

At 4940, as a function of the vibration in the phononic resonator, thesecond lightwave can be amplified.

What has been described above includes examples of one or moreembodiments. It is, of course, not possible to describe everyconceivable modification and alteration of the above structures ormethodologies for purposes of describing the aforementioned aspects, butone of ordinary skill in the art can recognize that many furthermodifications and permutations of various aspects are possible.Accordingly, the described aspects are intended to embrace all suchalterations, modifications, and variations that fall within the spiritand scope of the appended claims. Furthermore, to the extent that theterm “includes” is used in either the details description or the claims,such term is intended to be inclusive in a manner similar to the term“comprising” as “comprising” is interpreted when employed as atransitional word in a claim.

What is claimed is:
 1. A method for making an acousto-optical device,comprising: depositing an insulating layer on a substrate; forming awaveguiding member on the insulating layer; depositing a membrane layeron the insulating layer and on the waveguiding member such that thedeposited membrane layer abuts and overlies the waveguiding member;removing such of the membrane layer as overlies the waveguiding member;patterning the membrane layer so as to define therein at least onelongitudinally extensive phononic resonator traversed by the waveguidingmember; and removing at least a portion of the insulating layer thatunderlies the membrane layer, including such portion as underlies thelongitudinally extensive phononic resonator or resonators.
 2. The methodof claim 1, wherein the substrate is silicon, the insulating layer issilicon dioxide, the waveguiding member is silicon, and the membranelayer is silicon nitride.
 3. The method of claim 1, wherein, in responseto a first pulse and a second pulse being injected into the waveguidingmember, the membrane layer is conformed so as to convey phonons in adirection transverse to an optical direction of the waveguiding member.4. The method of claim 3, wherein the phononic resonator is conformed toreflect phonons through the membrane in a direction toward thewaveguiding member.
 5. The method of claim 1, wherein the patterning ofthe membrane layer is carried out so as to form a first slot and asecond slot on opposing sides of the waveguide member.